$\gamma$- BCK algebras
We know that $\Gamma-$ring, $\Gamma-$incline, $\Gamma-$semiring, $\Gamma-$semigroup are generalizations ofring, incline, semiring and semigroup respectively. In this paper, we introduce the concept of $\Gamma-$BCK-algebras as a generalization of BCK-algebras and study $\Gamma-$BCK-algebras. We also...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2022-11-01
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| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_3360_c7ccfa24ae9c04d2f4a786b35f1867e6.pdf |
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| Summary: | We know that $\Gamma-$ring, $\Gamma-$incline, $\Gamma-$semiring, $\Gamma-$semigroup are generalizations ofring, incline, semiring and semigroup respectively. In this paper, we introduce the concept of $\Gamma-$BCK-algebras as a generalization of BCK-algebras and study $\Gamma-$BCK-algebras. We also introduce subalgebra, ideal, closed ideal, normal subalgebra, normal ideal and construct quotient of $\Gamma-$BCK-algebras. We prove that if $f: M\to L$ be a normal homomorphism of $\Gamma-$BCK-algebras $M$ and $N,$ then $\Gamma-$BCK-algebra $M/N$ is isomorphic to $Im (f)$ where $N =Ker (f).$ |
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| ISSN: | 2251-7952 2645-4505 |